Some of the most efficacious antiviral therapeutics are ribonucleos(t)ide analogs. The presence of a 3'-to-5' proofreading exoribonuclease (ExoN) in coronaviruses diminishes the potency of many ribonucleotide analogs. The ability to interfere with ExoN activity will create new possibilities for control of SARS-CoV-2 infection. ExoN is formed by a 1:1 complex of nsp14 and nsp10 proteins. We have purified and characterized ExoN using a robust, quantitative system that reveals determinants of specificity and efficiency of hydrolysis. Double-stranded RNA is preferred over single-stranded RNA. Nucleotide excision is distributive, with only one or two nucleotides hydrolyzed in a single binding event. The composition of the terminal basepair modulates excision. A stalled SARS-CoV-2 replicase in complex with either correctly or incorrectly terminated products prevents excision, suggesting that a mispaired end is insufficient to displace the replicase. Finally, we have discovered several modifications to the 3'-RNA terminus that interfere with or block ExoN-catalyzed excision. While a 3'-OH facilitates hydrolysis of a nucleotide with a normal ribose configuration, this substituent is not required for a nucleotide with a planar ribose configuration such as that present in the antiviral nucleotide produced by viperin. Design of ExoN-resistant, antiviral ribonucleotides should be feasible.